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Catalan numbers are known to count noncrossing set partitions, while Narayana and Kreweras numbers refine this count according to the number of blocks in the set partition, and by its collection of block sizes. Motivated by reflection group generalizations of Catalan numbers and their q-analogues, this paper concerns a definition of q-Kreweras numbers for finite Weyl groups W, refining the q-Catalan numbers for W, and arising from work of the second author. We give explicit formulas in all types for the q-Kreweras numbers. In the classical types A, B, C, we also record formulas for the q-Narayana numbers and in the process show that the formulas depend only on the Weyl group (that is, they coincide in types B and C). In addition, we verify that in the classical types A, B, C, D the q-Kreweras numbers obey the expected cyclic sieving phenomena when evaluated at appropriate roots of unity.
相似文献
H*( Be ) ?L*V {H^*}\left( {{\mathcal{B}_e}} \right) \otimes {\Lambda^*}V 相似文献
14.
We establish a general relation between the statistics of the local Green’s function for systems with chaotic wave scattering and uniform energy loss (absorption) and the two-point correlator of its resolvents for the same system without absorption. Within the random matrix approach, this kind of a fluctuation dissipation relation allows us to derive the explicit analytic expression for the joint distribution function of the real and imaginary part of the local Green’s function for all symmetry classes as well as at an arbitrary degree of time-reversal symmetry breaking in the system. The outstanding problem of orthogonal symmetry is further reduced to simple quadratures. The results can be applied, in particular, to the experimentally accessible impedance and reflection in a microwave cavity attached to a single-mode antenna. 相似文献
15.
We review the derivation of generalised TAP equations for general quantum spin systems and apply the theory to a simple induced-moment spin glass model. We consider two-level systems with a singlet ground state and a triplet excited state, which interact via long range random exchange couplings. For not too large energy splitting the spin glass state can be stabilised. 相似文献
16.
The heat capacities of LaCl3, PrCl3, and NdCl3 have been measured from 5 to 350 K by adiabatic calorimetry. No co-operative thermal anomalies were seen in the temperature range investigated but substantial magnetic heat-capacity contributions of the non-cooperative (Schottky) type were found. Subtraction of the heat capacity of the diamagnetic and isostructural LaCl3 from those of the paramagnetic members yields experimental Schottky heat-capacity contributions which are compared with heat capacities derived from spectroscopically determined energy levels. Small discrepancies between the calculated and experimental contributions are probably due to differences in lattice heat capacities between LaCl3 and the others. The values of {(So(298.15 K) ? So(0)}/calth K?1 mol?1 are for LaCl3 and NdCl3, 32.88 and 36.67. Due to the possibility of a low-temperature phase transition, the entropy of PrCl3 covers only the experimental range of this research and that of Colwell, Mangum, and Utton. {So(298.15 K) ? So(0.294 K)} for PrCl3 is 36.64 calth K?1 mol?1. 相似文献
17.
It has been speculated that the application of nanofluids in real systems could lead to smaller, more compact heat exchangers
and reductions in material cost. However, few studies have been conducted which have carefully measured the thermo-physical
properties and thermal performance of these fluids as well as examine the system-level effects of using these fluids in traditional
cooling systems. In this study, dilute suspensions of 10 nm aluminum oxide nanoparticles in propanol (0.5, 1, and 3 wt%) were
investigated. Changes in density, specific heat, and thermal conductivity with particle concentration were measured and found
to be linear, whereas changes in viscosity were nonlinear and increased sharply with particle loading. Nanofluid heat transfer
performance data were generally commensurate with that measured for the baseline. For the 1 wt% concentration, a small but
significant enhancement in the heat transfer coefficient was recorded for 1800 < Re < 2800, which is attributed to an earlier
transition to turbulent flow. In the case of high particle loading (i.e. 3 wt%), the thermal performance was observed to deteriorate
with respect to the baseline case. Discoloration of the fluid was also observed after being cycled at high flow rates and
increased temperature. 相似文献
18.
Three experiments were conducted to examine the effects of trial-to-trial variations in speaking style, fundamental frequency, and speaking rate on identification of spoken words. In addition, the experiments investigated whether any effects of stimulus variability would be modulated by phonetic confusability (i.e., lexical difficulty). In Experiment 1, trial-to-trial variations in speaking style reduced the overall identification performance compared with conditions containing no speaking-style variability. In addition, the effects of variability were greater for phonetically confusable words than for phonetically distinct words. In Experiment 2, variations in fundamental frequency were found to have no significant effects on spoken word identification and did not interact with lexical difficulty. In Experiment 3, two different methods for varying speaking rate were found to have equivalent negative effects on spoken word recognition and similar interactions with lexical difficulty. Overall, the findings are consistent with a phonetic-relevance hypothesis, in which accommodating sources of acoustic-phonetic variability that affect phonetically relevant properties of speech signals can impair spoken word identification. In contrast, variability in parameters of the speech signal that do not affect phonetically relevant properties are not expected to affect overall identification performance. Implications of these findings for the nature and development of lexical representations are discussed. 相似文献
19.
The behavior of water droplets on aluminum surfaces with parallel grooves tens of microns in width and depth is considered, and a mechanistic model is developed for predicting the critical droplet size-droplets at incipient sliding due to gravity. The critical droplet size is nearly 50% smaller on micro-grooved surfaces than on the same surface without micro-grooves. The application of existing models fails to predict this behavior, and a new model based on empiricism is developed. The new model provides reasonable predictions of the critical droplet size for a given inclination angle, advancing contact angle, and maximum contact angle. When the grooves are aligned parallel to gravity, the maximum apparent contact angle does not occur at the advancing front but rather along the side of the droplet because of contact-line pinning. Droplets on these surfaces are elongated and possess a parallel-sided base contour shape. Novel data are provided for droplets in a Wenzel state, a Cassie-Baxter state, and combined state on micro-grooved surfaces, and the ability of the empirical model to handle these variations is explored. These findings may be important to a broad range of engineering applications. 相似文献
20.
U. Pustogowa C. Blaas C. Uiberacker J. Zabloudil P. Weinberger L. Szunyogh C. Sommers 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,16(4):653-658
The magnetic properties of (ConPdm)r superstructures on Pd(100) and Pd(111) are evaluated using the fully-relativistic spin-polarized screened Korringa-Kohn-Rostoker
method. It is found that only in the case of a Pd(111) substrate such superstructures exhibit perpendicular magnetism, while
on a Pd(100) substrate the magnetization is oriented in-plane. Also investigated is the effect of interdiffusion in repeated
superstructures. By using the inhomogeneous coherent potential approximation (CPA) for layered systems the effect of ordering
into (repeated) superstructures can be described in an ab-initio-like manner. It is found that already small amounts of interdiffusion can be decisive for the actual value of the magnetic
anisotropy energy.
Received 3 November 1999 and Received in final form 18 January 2000 相似文献
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